Related papers: Sparse covariance thresholding for high-dimensiona…
Given $n$ noisy samples with $p$ dimensions, where $n \ll p$, we show that the multi-step thresholding procedure based on the Lasso -- we call it the {\it Thresholded Lasso}, can accurately estimate a sparse vector $\beta \in {\mathbb R}^p$…
Lasso is a popular and efficient approach to simultaneous estimation and variable selection in high-dimensional regression models. In this paper, a robust LAD-lasso method for multiple outcomes is presented that addresses the challenges of…
This paper investigates covariance operator estimation via thresholding. For Gaussian random fields with approximately sparse covariance operators, we establish non-asymptotic bounds on the estimation error in terms of the sparsity level of…
We provide a novel -- and to the best of our knowledge, the first -- algorithm for high dimensional sparse regression with constant fraction of corruptions in explanatory and/or response variables. Our algorithm recovers the true sparse…
Selection of covariates is crucial in the estimation of average treatment effects given observational data with high or even ultra-high dimensional pretreatment variables. Existing methods for this problem typically assume sparse linear…
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…
Sparse linear regression is a fundamental problem in high-dimensional statistics, but strikingly little is known about how to efficiently solve it without restrictive conditions on the design matrix. We consider the (correlated) random…
We consider the problem of estimating high-dimensional covariance matrices of a particular structure, which is a summation of low rank and sparse matrices. This covariance structure has a wide range of applications including factor analysis…
Classification with a sparsity constraint on the solution plays a central role in many high dimensional machine learning applications. In some cases, the features can be grouped together so that entire subsets of features can be selected or…
Lasso and other regularization procedures are attractive methods for variable selection, subject to a proper choice of shrinkage parameter. Given a set of potential subsets produced by a regularization algorithm, a consistent model…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
This paper considers errors-in-variables models in a high-dimensional setting where the number of covariates can be much larger than the sample size, and there are only a small number of non-zero covariates. The presence of measurement…
In this paper, we introduce ``UniLasso'' -- a novel statistical method for sparse regression. This two-stage approach preserves the signs of the univariate coefficients and leverages their magnitude. Both of these properties are attractive…
It is known that the Thresholded Lasso (TL), SCAD or MCP correct intrinsic estimation bias of the Lasso. In this paper we propose an alternative method of improving the Lasso for predictive models with general convex loss functions which…
This paper is concerned with high-dimensional panel data models where the number of regressors can be much larger than the sample size. Under the assumption that the true parameter vector is sparse we propose a panel-Lasso estimator and…
In many social, economical, biological and medical studies, one objective is to classify a subject into one of several classes based on a set of variables observed from the subject. Because the probability distribution of the variables is…
We study the limitations of the well known LASSO regression as a variable selector when there exists dependence structures among covariates. We analyze both the classic situation with $n\geq p$ and the high dimensional framework with $p>n$.…
Inference and Estimation in Missing Information (MI) scenarios are important topics in Statistical Learning Theory and Machine Learning (ML). In ML literature, attempts have been made to enhance prediction through precise feature selection…
The interest in variable selection for clustering has increased recently due to the growing need in clustering high-dimensional data. Variable selection allows in particular to ease both the clustering and the interpretation of the results.…
When we are interested in high-dimensional system and focus on classification performance, the $\ell_{1}$-penalized logistic regression is becoming important and popular. However, the Lasso estimates could be problematic when penalties of…